A straight line drawing of a
planar graph is a plane
drawing where each edge is drawn using a straight line segment. Since all
edges are line segments, the drawing is completely determined by the placement
of vertices in the plane. chrobak_payne_straight_line_drawing uses an
algorithm of Chrobak and Payne
[71]
to form a straight
line drawing of a planar graph by mapping all n vertices in a planar
graph to integer coordinates in a (2n - 4) x (n - 2) grid.

The input graph passed to chrobak_payne_straight_line_drawing must
be a maximal planar graph with at least
3 vertices. Self-loops and parallel edges are ignored by this function. Note
that the restriction that the graph be maximal planar does not
mean that this function can only draw maximal planar graphs (the graph pictured
above is not maximal planar, for example). If you want to
draw a graph g, you can create a copy g' of g, store a
mapping m of vertices in g' to vertices in g,
triangulateg', and then send
g' in as the input to chrobak_payne_straight_line_drawing. The
drawing returned can then be applied to g using m to translate
vertices from one graph to another, since g contains a subset of the
edges in g'.

Complexity

If the vertex index map provides constant-time access to indices, this
function takes time O(n + m) for a planar graph with n vertices
and m edges. Note that
in a simple planar graph with f faces, m edges, and n
vertices, both f and m are O(n).

Parameters

A ForwardIterator that has value_type equal to
graph_traits<Graph>::vertex_descriptor.

OUT: PositionMap

A Writable LValue Property
Map that models the Position Map concept. The Position Map concept requires
that the value mapped to be an object that has members x and
y. For example, if p models PositionMap and v
is a vertex in the graph, p[v].x and p[v].y are valid
expressions. The type of x and y must be implicitly
convertable to std::size_t.

IN: VertexIndexMap vm

A Readable Property Map
that maps vertices from g to distinct integers in the range
[0, num_vertices(g) )Default: get(vertex_index,g)